The infinitive is often used after be (is,am, are, was and were) to talk about an agreement or an arrangement. It may also be used to give an order or to express a complaint.

You are to learn the poem by heart. (Order)
The committee is to meet on the 15th of February. (Arrangement)
John and Alice are to be married next month. (Arrangement)
How long are we to wait like this? (Complaint)

Subject + verb + object + infinitive

In this construction, the infinitive represents a completed action.

I saw the child cross the road. (As I looked on, the child crossed the road from one side to the other. Here I see the whole action.)
Did any one see him leave the house?
We heard her sing a lovely song.
They made the child drink the soup.

Subject + verb + object + present participle

In this construction the present participle represents an action that is going on and not completed.

I saw the child crossing the road. (I didn’t see the whole action.)
Did any one see him leaving the house?
We heard her singing a lovely song.

Subject + verb + infinitive phrase

Automation has come to stay.
Byron awoke one morning to find himself famous.
The poor woman awoke to find her husband gone.

The infinitive phrases can be changed into coordinate clauses.

Byron awoke one morning and found himself famous.